Koszuality of the \mathcal V^(d) dioperad

2017/12/13 by Poirier, Kate, Tradler, Thomas
#18D50 #55P48 #Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1712.04975

Abstract

Define a \mathcal V^(d)-algebra as an associative algebra with a symmetric and invariant co-inner product of degree d. Here, we consider \mathcal V^(d) as a dioperad which includes operations with zero inputs. We show that the quadratic dual of \mathcal V^(d) is (\mathcal V^(d))^!=\mathcal V^(-d) and prove that \mathcal V^(d) is Koszul. We also show that the corresponding properad is not Koszul contractible.

Related

• Koszul duality for dioperads
• Associator dependent algebras and Koszul duality
• The Koszul complex is the cotangent complex
• Distributive Laws and the Koszulness
• The Operad Quad is Koszul